2.3 Cosine Graphs

Cosine Graphs

Plot of Cosine

Cosine is just like Sine, but it starts at 1 and heads down until π radians (180°) and then heads up again.

SECANT

Secant also known as sec, are the graph for 1/cosine.

The secant function has asymptotes at $\frac{\pi}{2}\pm n\pi$π2​±nπ. It is periodic with period $2\pi$2π. It takes no values in the open interval between $-1$−1 and $1$1. It has local minima at $0\pm2n\pi$0±2nπ and local maxima at $\pi\pm2n\pi$π±2nπ. These correspond with the maxima and minima respectively of the cosine function since, by definition, $\sec x=\frac{1}{\cos x}$secx=1cosx​. 

The function $\sec x$secx is an even function, meaning $\sec(-x)=\sec x$sec(−x)=secx for all values of $x$x. This follows from the fact that $\cos x$cosx is an even function.

From the corresponding relations between the sine and cosine functions, we see that $\sec x=\csc\left(\frac{\pi}{2}-x\right)=-\csc\left(x-\frac{\pi}{2}\right)$secx=csc(π2​−x)=−csc(x−π2​). This identity shows that the graph of $\sec x$secx is obtained from the graph of $\csc x$cscx by shifting it to the right by $\frac{\pi}{2}$π2​ and reflecting it in the $x$x-axis.